What are the dimension of a garden that is 72 square feet with a perimeter of 36 feet?

Answer 1

Assuming a rectangular garden it is 6 ft by 12 ft.

perimeter = 2 x (width + length)

→ length = perimeter ÷ 2 - width

= 36ft ÷ 2 - width

= 18 - width ft

area = width x length

→ 72 sq ft = width x (18 - width) sq ft

→ 72 = 18 x width - width2

→ width2 - 18 width + 72 = 0

→ (width - 6)(width - 12) = 0

→ width = 6 → length = 18 - 6 = 12

or width = 12 → length = 18 - 12 = 6

→ garden is 6 ft by 12 ft.

If it's L shaped (like our neighbour's garden - the bottom part of our garden was sold to them many-many-many years ago so that their garden stretches round the bottom of ours), it could have an infinite number of sets of side lengths, eg the side lengths could be:

• {9 ft, 6 ft, 3 ft, 3 ft, 6 ft, 9 ft} ie a 9 ft square with a 3 ft square missing from one corner.
• {11 ft, 6 ft, 5 ft, 1 ft, 6 ft, 7ft} ie an 11 ft x 7 ft rectangle with a 1 ft x 5 ft rectangle missing from one corner.
• {11 ft, 2 ft, 1 ft, 5 ft, 10 ft, 7 ft} ie an 11 ft x 7 ft rectangle with a 5 ft x 1 ft rectangle missing from one corner.
• etc.